Given the use of "praying" and "prophesying" in chapter 14, I think we are bound to take these actions as expressions of charismatic gifts in the assembly. These certainly bear an analogy to ordinary acts of worship, but in the context the apostle's description of what was happening in Corinth must have been made worse by the fact that these women were actually presuming to speak on behalf of God.
I don’t understand why you say “presuming to speak on behalf of God”. I believe the bible presents that during NT times there were indeed genuine female prophetesses who did indeed speak on behalf of God via inspiration (Acts 2:16-18, Acts 21:9, Luke 2:36-38). I don’t see a reason to assume that Paul was not addressing a legitimate use of the spiritual gift.
Paul does not link headship with headcovering per se, he links headship with headcovering while praying or prophesying.
If he does this specifically, then a dilemma is created, in that he would be specifically authorising the woman to pray and prophesy when it is his intention to forbid her to speak at all. Given his eventual prohibition it is more natural to take his words as an example of a lack of decorum in public rather than the specific action to which he is confining his instructions.
I would respectfully submit that this reading does cause far greater strain to the text than the one I suggest. I think it can be established that Paul’s purpose in 1 Cor 11 it to address the issue of headcoverings, not the propriety of prophesying (v 6, 10). As such, why would Paul confuse his audience by giving the example of headcovering while performing a prohibited activity? It would serve only to confuse because readers would not know which activity was wrong – being uncovered or prophesying.
I do not believe any dilemma or contradiction is created by the reading I have suggested (i.e. Paul is regulating the use of inspired prophecy by women) because I do not believe Paul does “forbid her to speak at all”. Paul’s words in 1 Cor 14:34 should be understood as forbidding not all speech, but a specific kind of speech that would allow exceptions.
1) Even the “strictest” reformed churches I know allow women to sing during the assembly in accordance with Eph 5:19 and Col 3:16, so that already shows in practice they do not understand “keep silence in the churches” as an absolute command with no exceptions.
2) Paul already used the phase “keep silence in the church” in 1 Cor 14:28 with respect to a man with the gift of tongues but no interpreter. Was Paul forbidding that man to even open his mouth when there was no interpreter? Or was Paul forbidding a particular kind of speech – the use of his gift of tongues?. If the man did not use is gift of tongues surely he would have been free to speak (as was appropriate for his office).
So by the bible’s own definition, the phase “keep silence” in 1 Cor 14 is not meant to be understood in an absolute way.
3) If what is under consideration here is inspired prophecy, - and yourself have said that in the context of 1 Corinthians “prayer and prophecy” must be some form of charismatic gift- how can it be an appropriate reply to an inspired prophetess to tell her to “ask her husband at home”? You might tell her that now is not the time to exercise her gift, but it makes no sense to tell her to ask her husband. Again, inspired prophecy is not the kind of speech Paul is seeking to forbid.
4) Paul’s command in 1 Cor 14:34 says “as also saith the Law”. So the NT regulation is similar to that in the OT. And the OT law itself allowed for female prophetesses to teach and have authority in Israel, be it Miriam, Deborah, Huldah or Anna.
I do see enough evidence that 1 Cor 14:34 is not meant to be absolute, such that I think 1 Cor 11 can be seen as Paul making an exception for inspired prophetesses. He just required them to wear a covering as a sign of their submission to the normal order.